Changing between multiple Microsoft Teams accounts within the app or browser
Hello
So technically you don't have two organization accounts. You have one account and your home organization. Then this same work account is also a guest user in another organization. This 2nd one is more like a persona, not its own full organization account.
If you have already accepted the invitation to join the other organization, when you click on the user profile icon on the upper right in Teams, you should see something similar to mine in the screenshot:
ets (green arrow) is my home organization. "Microsoft" (red arrow) is the organization I am invited to as a guest user. So, when I need to see messages and channels/teams in the Microsoft organization where I am a guest, I just click on "Microsoft" to switch over. When I am done there, you click on the user profile icon again, and you will see your home organization you can click on to switch back to your home org.